A Multi-Model Ensemble Kalman Filter for Data Assimilation and Forecasting

Eviatar Bach (1) , Michael Ghil (1)

1 LMD - Laboratoire de Météorologie Dynamique (UMR 8539)

Data assimilation (DA) aims to optimally combine model forecasts and observations that are both partial and noisy. Multi-model DA generalizes the variational or Bayesian formulation of the Kalman filter, and we prove that it is also the minimum variance linear unbiased estimator. Here, we formulate and implement a multi-model ensemble Kalman filter (MM-EnKF) based on this framework. The MM-EnKF can combine multiple model ensembles for both DA and forecasting in a flow-dependent manner; it uses adaptive model error estimation to provide matrix-valued weights for the separate models and the observations. We apply this methodology to various situations using the Lorenz96 model for illustration purposes. Our numerical experiments include multiple models with parametric error, different resolved scales, and different fidelities. The MM-EnKF results in significant error reductions compared to the best model, as well as to an unweighted multi-model ensemble, with respect to both probabilistic and deterministic error metrics.

Mots clés: ensemble Kalman filter; multi-model ensemble; Statistics - Methodology; Electrical Engineering and Systems Science - Systems and Control; Mathematics - Optimization and Control; Physics - Atmospheric and Oceanic Physics

Domaines: Planète et Univers [physics]

Eviatar Bach, Michael Ghil. A Multi-Model Ensemble Kalman Filter for Data Assimilation and Forecasting. Journal of Advances in Modeling Earth Systems, 2023, 15, ⟨10.1029/2022MS003123⟩. ⟨insu-03993953⟩